scholarly journals Passive Dynamic Bounding Control using Symmetry Condition Control Laws

2019 ◽  
pp. 451-457
Author(s):  
P. Murali Krishna ◽  
R. Prasanth Kumar
Keyword(s):  
Fixed Points ◽  
Initial Conditions ◽  
Legged Locomotion ◽  
Zero Energy ◽  
Additional Energy ◽  
Control Laws ◽  
Quadruped Robots ◽  
Existence And Stability ◽  
The Stability ◽  
Bounding Gait

Legged locomotion is preferred over the wheeled locomotion as it can be used both for flat and rough terrains. Quadruped robots are preferred since they can offer better stability with considerable reliability. In recent years, passive dynamics has been used to obtain near zero-energy bounding gaits. Although theoretically such gaits consume no energy, in practice some additional energy is required to overcome losses. Existence and stability of such gaits have been thoroughly studied in literature for quadruped models with the assumption that the mass distribution and stiffness in the front and back legs are symmetric. Fixed points found using Poincare map indicate touchdown angle-liftoff angle symmetry between front and back legs. This property can be used to search for fixed points with ease. However, the range of initial conditions where the bounding gait is stable is highly limited. Control laws based on symmetry conditions observed are proposed in this paper to improve the stability region. One such control law based on body-fixed touchdown angles theoretically allows redesign of quadruped robot with physical cross coupling between legs to achieve inherent stability without leg actuation.

scholarly journals A Bio-Inspired Compliance Planning and Implementation Method for Hydraulically Actuated Quadruped Robots with Consideration of Ground Stiffness

Sensors ◽  
2021 ◽  
Vol 21 (8) ◽  
pp. 2838
Author(s):  
Xiaoxing Zhang ◽  
Haoyuan Yi ◽  
Junjun Liu ◽  
Qi Li ◽  
Xin Luo
Keyword(s):  
Harmonic Oscillation ◽  
Ground Surface ◽  
Legged Locomotion ◽  
Soft Ground ◽  
Quadruped Robots ◽  
In Series ◽  
Reaction Forces ◽  
Implementation Method ◽  
The Stability ◽  
Natural Dynamics

There has been a rising interest in compliant legged locomotion to improve the adaptability and energy efficiency of robots. However, few approaches can be generalized to soft ground due to the lack of consideration of the ground surface. When a robot locomotes on soft ground, the elastic robot legs and compressible ground surface are connected in series. The combined compliance of the leg and surface determines the natural dynamics of the whole system and affects the stability and efficiency of the robot. This paper proposes a bio-inspired leg compliance planning and implementation method with consideration of the ground surface. The ground stiffness is estimated based on analysis of ground reaction forces in the frequency domain, and the leg compliance is actively regulated during locomotion, adapting them to achieve harmonic oscillation. The leg compliance is planned on the condition of resonant movement which agrees with natural dynamics and facilitates rhythmicity and efficiency. The proposed method has been implemented on a hydraulic quadruped robot. The simulations and experimental results verified the effectiveness of our method.

CHAOTIC BEHAVIOR AND DYNAMICS OF MAPS USED IN A METHOD OF SCRAMBLING SIGNALS

2010 ◽  
Vol 20 (12) ◽  
pp. 4097-4101
Author(s):  
REZA MAZROOEI-SEBDANI ◽  
MEHDI DEHGHAN
Keyword(s):  
Fixed Points ◽  
Limit Cycles ◽  
Secure Communication ◽  
Chaotic Behavior ◽  
Initial Conditions ◽  
Chaotic Encryption ◽  
Input And Output ◽  
Sensitive Dependence ◽  
Close Relationship ◽  
Existence And Stability

The close relationship between chaos and cryptography makes chaotic encryption a natural candidate for secure communication and cryptography. In this manuscript, we prove that a class of maps that have been proposed as suitable for scrambling signals possess the property of sensitive dependence on initial conditions (s.d.i.c.) necessary for chaos and cryptography. Our result can also be used for generating other maps with s.d.i.c., through a suitable semiconjugacy between their input and output parts. Using the condition of semiconjugacy we also establish for this class of maps rigorous criteria for the existence and stability of their fixed points and limit cycles.

The Existence and Stability of Ultraharmonics and Subharmonics in Forced Nonlinear Oscillations

1954 ◽  
Vol 21 (4) ◽  
pp. 327-335
Author(s):  
T. K. Caughey
Keyword(s):  
Nonlinear Oscillations ◽  
Initial Conditions ◽  
Forced Oscillations ◽  
Order System ◽  
Response Curves ◽  
Restoring Force ◽  
Amplitude Frequency Response ◽  
Existence And Stability ◽  
Linearized Theory ◽  
The Stability

Abstract A study is made of the forced oscillations of a second-order system having a small cubic nonlinearity in the restoring force. It is shown that under suitable conditions ultraharmonic or subharmonic motion exists in addition to the harmonic motion which a linearized theory would predict. By studying the stability of such motions it is shown that at points on the amplitude frequency-response curves having vertical tangents, instability and consequently “jumps” occur. A study of the dependence of the motion on the initial conditions reveals that while ultra-harmonic and harmonic motions are rather insensitive to initial conditions, the existence of subharmonic motion can be achieved only for a restricted set of initial conditions.

scholarly journals Dynamical analysis of anisotropic inflation

2016 ◽  
Vol 31 (21) ◽  
pp. 1640002 ◽  
Author(s):  
Mindaugas Karčiauskas
Keyword(s):  
Vector Field ◽  
Phase Space ◽  
Fixed Points ◽  
Initial Conditions ◽  
Dynamical Analysis ◽  
Curvature Perturbation ◽  
Bianchi I ◽  
Anisotropic Curvature ◽  
Primordial Magnetic Fields ◽  
The Stability

The inflaton coupling to a vector field via the [Formula: see text] term is used in several contexts in the literature, such as to generate primordial magnetic fields, to produce statistically anisotropic curvature perturbation, to support anisotropic inflation, and to circumvent the [Formula: see text]-problem. In this work, I perform dynamical analysis of this system allowing for the most general Bianchi I initial conditions. I also confirm the stability of attractor fixed points along phase–space directions that had not been investigated before.

scholarly journals Existence and Stability Results for Second-Order Neutral Stochastic Differential Equations With Random Impulses and Poisson Jumps

2021 ◽  
Vol 1 (1) ◽  
pp. 1-18
Author(s):  
K. Ravikumar ◽  
K. Ramkumar ◽  
Dimplekumar Chalishajar
Keyword(s):  
Differential Equations ◽  
Initial Conditions ◽  
Mild Solutions ◽  
Functional Differential Equations ◽  
Banach Contraction ◽  
Existence And Stability ◽  
Random Impulses ◽  
Functional Differential ◽  
The Stability ◽  
Stability Results

The objective of this paper is to investigate the existence and stability results of secondorder neutral stochastic functional differential equations (NSFDEs) in Hilbert space. Initially, we establish the existence results of mild solutions of the aforementioned system using the Banach contraction principle. The results are formulated using stochastic analysis techniques. In the later part, we investigate the stability results through the continuous dependence of solutions on initial conditions.

scholarly journals Vibration Control of Nonlinear Three‐dimensional Marine Riser Model with Output Constraints

2021 ◽  
Author(s):  
Min Wan ◽  
Yanxia Yin ◽  
Jun Liu ◽  
Xiaoqiang Guo
Keyword(s):  
Differential Equations ◽  
Initial Conditions ◽  
External Disturbance ◽  
Three Dimensional ◽  
Distributed Parameter ◽  
Marine Riser ◽  
Control Laws ◽  
Finite Dimensional ◽  
Output Constraints ◽  
The Stability

Abstract A typical three-dimensional flexible marine riser which is described by a distributed parameter system with several partial differential equations and ordinary differential equations is considered in this paper, we are aiming at limiting the top displacement of riser within restricted ranges. Appropriate boundary controls by integrating finite-dimensional backstepping technique with barrier Lyapunov functions are put forwarded to suppress the vibration of flexible riser under the external disturbance. The stability of the closed-loop system with the designed boundary control laws is proved by Lyapunov’s synthetic method without any discretization or simplification of the dynamic in the time and space when the initial conditions are satisfied. Furthermore, in order to illustrate the effectiveness of proposed controls laws, numerical simulation studies are carried.

Institutional Reforms and Interaction of Local Governments

2015 ◽  
Vol 3 (2) ◽  
pp. 25-33
Author(s):  
Georges Sarafopoulos ◽  
Panagiotis G. Ioannidis
Keyword(s):  
Nash Equilibrium ◽  
Local Governments ◽  
Complex Dynamics ◽  
Initial Conditions ◽  
Replicator Dynamics ◽  
Discrete Dynamical System ◽  
Period Doubling ◽  
Box Dimension ◽  
Existence And Stability ◽  
The Stability

The paper considers the interaction between regions during the implementation of a reform, on regional development through a discrete dynamical system based on replicator dynamics. The existence and stability of equilibria of this system are studied. The authors show that the parameter of the local prosperity may change the stability of equilibrium and cause a structure to behave chaotically. For the low values of this parameter the game has a stable Nash equilibrium. Increasing these values, the Nash equilibrium becomes unstable, through period-doubling bifurcation. The complex dynamics, bifurcations and chaos are displayed by computing numerically Lyapunov numbers, sensitive dependence on initial conditions and the box dimension.

Design and Implementation of a Leg–Wheel Robot: Transleg

2017 ◽  
Vol 9 (5) ◽  
Author(s):  
Zhong Wei ◽  
Guangming Song ◽  
Guifang Qiao ◽  
Ying Zhang ◽  
Huiyu Sun
Keyword(s):  
Degrees Of Freedom ◽  
Legged Locomotion ◽  
The Body ◽  
Transmission Mechanism ◽  
Design And Implementation ◽  
Kinematic Analyses ◽  
Turning Motion ◽  
The Wire ◽  
The Stability ◽  
Bounding Gait

In this paper, the design and implementation of a novel leg–wheel robot called Transleg are presented. Transleg adopts the wire as the transmission mechanism to simplify the structure and reduce the weight. To the best knowledge of the authors, the wire-driven method has never been used in the leg–wheel robots, so it makes Transleg distinguished from the existing leg–wheel robots. Transleg possesses four transformable leg–wheel mechanisms, each of which has two active degrees-of-freedom (DOFs) in the legged mode and one in the wheeled mode. Two actuators driving each leg–wheel mechanism are mounted on the body, so the weight of the leg–wheel mechanism is reduced as far as possible, which contributes to improving the stability of the legged locomotion. Inspired by the quadruped mammals, a compliant spine mechanism is designed for Transleg. The spine mechanism is also actuated by two actuators to bend in the yaw and pitch directions. It will be beneficial to the turning motion in the legged and wheeled modes and the bounding gait in the legged mode. The design and kinematic analyses of the leg–wheel and spine mechanisms are presented in detail. To verify the feasibility of Transleg, a prototype is implemented. The experiments on the motions in the legged and wheeled modes, the switch between the two modes, and the spine motions are conducted. The experimental results demonstrate the validity of Transleg.

scholarly journals Stability-Guaranteed and High Terrain Adaptability Static Gait for Quadruped Robots

Sensors ◽  
2020 ◽  
Vol 20 (17) ◽  
pp. 4911
Author(s):  
Qian Hao ◽  
Zhaoba Wang ◽  
Junzheng Wang ◽  
Guangrong Chen
Keyword(s):  
Impedance Control ◽  
Stability Margin ◽  
Planning Method ◽  
Legged Robots ◽  
Gait Planning ◽  
Quadruped Locomotion ◽  
Quadruped Robots ◽  
Adjustment Strategy ◽  
Compliant Behavior ◽  
The Stability

Stability is a prerequisite for legged robots to execute tasks and traverse rough terrains. To guarantee the stability of quadruped locomotion and improve the terrain adaptability of quadruped robots, a stability-guaranteed and high terrain adaptability static gait for quadruped robots is addressed. Firstly, three chosen stability-guaranteed static gaits: intermittent gait 1&2 and coordinated gait are investigated. In addition, then the static gait: intermittent gait 1, which is with the biggest stability margin, is chosen to do a further research about quadruped robots walking on rough terrains. Secondly, a position/force based impedance control is employed to achieve a compliant behavior of quadruped robots on rough terrains. Thirdly, an exploratory gait planning method on uneven terrains with touch sensing and an attitude-position adjustment strategy with terrain estimation are proposed to improve the terrain adaptability of quadruped robots. Finally, the proposed methods are validated by simulations.

scholarly journals Emergent chiral symmetry in a three-dimensional interacting Dirac liquid

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
András L. Szabó ◽  
Bitan Roy
Keyword(s):  
Fixed Points ◽  
Chiral Symmetry ◽  
Rotational Symmetry ◽  
Three Dimensional ◽  
Spatial Dimension ◽  
Dirac Fermions ◽  
Electronic Interactions ◽  
Emergent Phenomena ◽  
Ordered Phases ◽  
The Stability

Abstract We compute the effects of strong Hubbardlike local electronic interactions on three-dimensional four-component massless Dirac fermions, which in a noninteracting system possess a microscopic global U(1) ⊗ SU(2) chiral symmetry. A concrete lattice realization of such chiral Dirac excitations is presented, and the role of electron-electron interactions is studied by performing a field theoretic renormalization group (RG) analysis, controlled by a small parameter ϵ with ϵ = d−1, about the lower-critical one spatial dimension. Besides the noninteracting Gaussian fixed point, the system supports four quantum critical and four bicritical points at nonvanishing interaction couplings ∼ ϵ. Even though the chiral symmetry is absent in the interacting model, it gets restored (either partially or fully) at various RG fixed points as emergent phenomena. A representative cut of the global phase diagram displays a confluence of scalar and pseudoscalar excitonic and superconducting (such as the s-wave and p-wave) mass ordered phases, manifesting restoration of (a) chiral U(1) symmetry between two excitonic masses for repulsive interactions and (b) pseudospin SU(2) symmetry between scalar or pseudoscalar excitonic and superconducting masses for attractive interactions. Finally, we perturbatively study the effects of weak rotational symmetry breaking on the stability of various RG fixed points.

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